Differential equations

A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation: where * e = the natural logarithm base (also known as Euler's number), * x0 = the x-value of the sigmoid's midpoint, * L = the curve's maximum value, and * k = the steepness of the curve.

Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations.

A differential equation is a mathematical equation that relates some function with its derivatives.

In mathematics the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace (/ləˈplɑːs/).

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.

In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R (where U is an open subset of Rn) which satisfies Laplace's equation, i.

In mathematics, a Green's function is the impulse response of an inhomogeneous differential equation defined on a domain, with specified initial conditions or boundary conditions.

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: where k is a positive constant.

Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law.

Exponential growth is a phenomenon that occurs when the growth rate of the value of a mathematical function is proportional to the function's current value, resulting in its growth with time being an exponential function.

Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation.